Grain charges \(Ze\) , with \(e\)  being the electron charge, fluctuate stochastically due to the collection of electrons and the recombination of ions on their surfaces. The grain charge equilibrium [1]} can be written as
\(f(Z,\tau _k)(J_i(Z,\tau _k)+J_s(Z,\tau _k))=f(Z+1,\tau _k)J_\mathrm {e}(Z+1,\tau _k),\) 
